What types of New World plants were there in Middle-earth, and how did they get there?

A curious feature of Middle-earth is the fact that certain plants seem to grow there that really shouldn't. These are New World plants; crops, herbs, fruit and vegetables that weren't seen in the Old World before a few hundred years ago. In Tolkien's fiction, Middle-earth represents the Old World as it was millennia earlier than this, so in principle these plants shouldn't exist there. Especially with the release of the movie (and some related comments in the Movie-goer's Guide to The Fellowship of the Ring) there's been a lot of interest in these curiosities. Here, then, is a brief trip through the anomalous botany of Middle-earth.

Corn is mentioned several times, but in the books does not really represent a problem. As mentioned in the Movie-goer's Guide, when Tolkien writes about corn, he's writing about a grass cereal like wheat, and we can say this for certain because of a reference from The Two Towers. There Treebeard sings a song
of the Entwives that contains the line, 'When spring is come to garth and field, and corn is in the blade' (III 4 Treebeard). The expression 'in the blade' describes a young cereal plant that is yet to grow an ear, so we can be sure what is meant by the word 'corn'.

So Old World corn is simple to explain, or was until the movie appeared, because there it's shown as a quite different type of plant, maize, which could not have appeared in Middle-earth. This confusion only applies to the
film-makers' interpretation of Tolkien's words, though, so it's really just a minor movie matter.

Potatoes are rather harder to explain. They're obviously part of the hobbits' staple diet, and Sam even seems to expect to them to grow wild in Ithilien: '...I'd make him look for turnips and carrots, and taters too, if it was the time o' the year' (The Two Towers IV 4
Of Herbs and Stewed Rabbit - 'taters' is Sam's word for 'potatoes', as he explains himself).
It has been suggested that Sam's 'potatoes' weren't the same kind of vegetable as ours, but were
some other similar plant that later became extinct. To be frank, this seems unlikely, but not perhaps impossible.

Tobacco (or pipe-weed, to use the more correct term) has an explanation for its presence within the terms of the stories. It was brought to Middle-earth, apparently, aboard the ships of the
Númenóreans during the Second Age. Indeed, one of its many names is westmansweed, a reference to its origins across the western Sea. We'd have to presume that pipe-weed died out in Middle-earth some time after the War of the Ring, so that it had to be reintroduced thousands of years later.

This Númenórean explanation, by the way, might extend to potatoes, too. We might imagine them being brought to Middle-earth by the mariners of Númenor, later lost, and then reintroduced during the Age
of Discovery. It's important to note that Tolkien nowhere even hints at this possibility, though.

Tomatoes have an interesting history. The first editions of The Hobbit carried a passage where Gandalf calls to Bilbo, 'And just bring out the cold chicken and tomatoes!' (chapter 1 An Unexpected Party). In this case, Tolkien changed his mind about the reference, and later editions carry different text: 'And just bring out the cold chicken and pickles!' (ibid).